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Mechanics

Velocity and projectiles

Velocity is the vector quantity of speed. What this means is that it has both magnitude and direction. Speed is a scalar so it just has a magnitude.

In mechanics we can calculate the forces on all objects into just the x and y axis directions. In almost all cases the x and y forces are completely independent on each other and so calculations can be made independently.

We can calculate the current velocity of an object by knowing its initial velocity, acceleration and time.

From this equation many things can be found out aside from just velocity. For instance, on earth where  is the gravitational acceleration 9.8m  we can find out the maximum height of a projectile. This happens when , so the equation of the maximum height is derived from this.  Since the acceleration (9.8m ) is in the opposite direction to the initial velocity it becomes  which is . Of course this is only if the acceleration due to gravity is the only acceleration the object is undergoing.

Back to the original equation, from it we are about to calculate the velocity (in either the x or y axis) of a projectile at any point along its projection if we know its initial velocity, the accelerations it is undergoing and it’s change in displacement (along the x or y axis).

It is important to remember that the activities along each axis are independent.

The average velocity is calculated by the change in displacement over the change in time, , similarly the average acceleration is calculated by the change in velocity over the change in time.

It must be noted that the average velocity and average speed are often very different. For example, if an object does a 1km loop in 5 minutes and finishes at the same place as it started it has an average velocity of 0m/s yet its average speed is 3.33m/s.